ON η3( aτ) η3( bτ) WITH a+ b=8

Chan, Heng Huat; Cooper, S. Barry; Liaw, Wen-Chin

doi:10.1017/s144678870800058x

Cited by 9 publications

(6 citation statements)

References 9 publications

(10 reference statements)

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“…For the third entry in Theorem 5, we do not seem to obtain a reasonably concise integral involving K (due to the apparent lack of a parametrization for the degree 7 modular equation). Using the binary theta function for η 3 (τ )η 3 (7τ ) [4], we obtain the sum (m,n) =(0,0)…”

Section: Weight 3 Cases and Lattice Sumsmentioning

confidence: 99%

Moments of elliptic integrals and critical $$L$$ L -values

2014

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Section: Weight 3 Cases and Lattice Sumsmentioning

confidence: 99%

Moments of elliptic integrals and critical $$L$$ L -values

2014

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“…Remark 2.1. Identities (2.6)-(2.8) were first discovered and proved by Chan et al [1] using properties of spherical theta functions.…”

Section: Newforms Of Weight K >mentioning

confidence: 96%

On the vanishing of the coefficients of CM eta quotients

Huber,

Liu,

McLaughlin

et al. 2023

Proceedings of the Edinburgh Mathematical Society

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This work characterizes the vanishing of the Fourier coefficients of all CM (Complex Multiplication) eta quotients. As consequences, we recover Serre’s characterization about that of $\eta(12z)^{2}$ and recent results of Chang on the pth coefficients of $\eta(4z)^{6}$ and $\eta(6z)^{4}$ . Moreover, we generalize the results on the cases of weight 1 to the setting of binary quadratic forms.

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“…Principal Genus (1, 0, 162), (9,6,19), (9, −6, 19) +1 +1 Second Genus (2, 0, 81), (11,10,17), (11, −10, 17) −1 +1 . In the above table, p is taken to be coprime to −648 and represented by the given genus.…”

Section: Casementioning

confidence: 99%

“…(2) p is represented by the form (9,6,19) if and only if W −648 (x) factors into two irreducible cubic polynomials modulo p,…”

Section: Casementioning

confidence: 99%